Analyze Complex Modulation With Statistical Methods

Peak Power measurements once involved fairly simple calculations on pulsed waveforms occurring at some known duty cycle and pulse width. But modern modulated waveforms are often characterized by fairly complex power profiles, and peak power measurements may not be quite so straightforward. Fortunately, a six-page white paper from Boonton Electronics, "Analysis of Complex Modulated Carriers Using Statistical Methods," provides details on a diode-detectorbased measurement system and calibration scheme that can provide accurate measurement results even with digitally modulated carriers.

The white paper offers a block diagram for a measurement system that includes a diode detector with wide RF bandwidth and narrower video bandwidth, a high-speed analog-to-digital converter (ADC), and a digitally controlled continuous-wave (CW) power calibrator.

The power calibrator is designed to eliminate the errors associated with detector diode nonlinearities, creating a table of detector output values for a number of different precision power levels covering the effective dynamic range of the measurement system. Through interpolation, the calibration table is extended for all possible values of the ADC, which in turn yields the measured power for each sample of the detected RF input signal range.

Because amplitude and phase modulation are often combined in modern digital modulation schemes, the waveforms of these systems cannot be directly related to traditional modulation parameters, such as modulation depth and modulation index. For this reason, statistical analysis proves to be a useful tool in understanding the actual peak power values for different digital modulation schemes. The note explains the use of various statistical functions, including probability density functions (PDFs), cumulative density functions (CDFs), and complementary cumulative density functions (CCDFs) for performing accurate measurements of peak power on complex modulated carriers.